BayeSN-TD: Time Delay and $H_0$ Estimation for Lensed SN H0pe

TL;DR

BayeSN-TD introduces a hierarchical BayeSN-based framework augmented with a Gaussian-process microlensing model to jointly fit time delays and magnifications for multiply-imaged SNe Ia. By extending BayeSN with phase coverage to $85$ rest-frame days and implementing an achromatic microlensing GP with a Gibbs kernel, it yields robust time-delay posteriors that are well-calibrated in simulations and can be translated into $H_0$ constraints when combined with lens models. Applied to SN H0pe, BayeSN-TD finds time delays $\Delta T_{BA}=121.9^{+9.5}_{-7.5}$ days and $\Delta T_{BC}=63.2^{+3.2}_{-3.3}$ days with magnifications $\beta_A=2.38^{+0.72}_{-0.54}$, $\beta_B=5.27^{+1.25}_{-1.02}$, $\beta_C=3.93^{+1.00}_{-0.75}$, leading to $H_0=69.3^{+12.6}_{-7.8}$ km s$^{-1}$ Mpc$^{-1}$ (photometry) and $66.8^{+13.4}_{-5.4}$ km s$^{-1}$ Mpc$^{-1}$ (photometry+spectroscopy) when combined with lens models. While current precision is insufficient to resolve the Hubble tension, the method proves scalable for the growing glSN sample from LSST and future template data.

Abstract

We present BayeSN-TD, an enhanced implementation of the probabilistic type Ia supernova (SN Ia) BayeSN SED model, designed for fitting multiply-imaged, gravitationally lensed type Ia supernovae (glSNe Ia). BayeSN-TD fits for magnifications and time-delays across multiple images while marginalising over an achromatic, Gaussian process-based treatment of microlensing, to allow for time-dependent deviations from a typical SN Ia SED caused by gravitational lensing by stars in the lensing system. BayeSN-TD is able to robustly infer time delays and produce well-calibrated uncertainties, even when applied to simulations based on a different SED model and incorporating chromatic microlensing, strongly validating its suitability for time-delay cosmography. We then apply BayeSN-TD to publicly available photometry of the glSN Ia SN H0pe, inferring time delays between images BA and BC of $ΔT_{BA}=121.9^{+9.5}_{-7.5}$ days and $ΔT_{BC}=63.2^{+3.2}_{-3.3}$ days along with absolute magnifications $β$ for each image, $β_A = 2.38^{+0.72}_{-0.54}$, $β_B=5.27^{+1.25}_{-1.02}$ and $β_C=3.93^{+1.00}_{-0.75}$. Combining our constraints on time-delays and magnifications with existing lens models of this system, we infer $H_0=69.3^{+12.6}_{-7.8}$ km s$^{-1}$ Mpc$^{-1}$, consistent with previous analysis of this system; incorporating additional constraints based on spectroscopy yields $H_0=66.8^{+13.4}_{-5.4}$ km s$^{-1}$ Mpc$^{-1}$. While this is not yet precise enough to draw a meaningful conclusion with regard to the `Hubble tension', upcoming analysis of SN H0pe with more accurate photometry enabled by template images, and other glSNe, will provide stronger constraints on $H_0$; BayeSN-TD will be a valuable tool for these analyses.

Figures (11)

• Figure 1: Upper: Histogram showing distribution of time-delay residuals relative to true simulated values when applying BayeSN-TD to simulations of glSNe Ia observed by Roman presented in Pierel21. Lower: Cumulative density of time-delay residual normalised by posterior uncertainties (dashed) shown alongside the expected cumulative density function for a Normal distribution represented by the shaded region. This demonstrates that BayeSN-TD produces well-calibrated uncertainties for these simulations.
• Figure 2: Left panels: Simulated 2-image Roman glSN Ia light curve from Pierel24 along with associated BayeSN-TD fits. Right panels: Plotted data points represent simulated deviation from model light curves as a result of microlensing, with associated uncertainties from measurement noise as true simulated values post-microlensing, without noise, are not available. Plotted line and shaded region represent the posterior mean and standard deviation on microlensing from BayeSN-TD, demonstrating that with Roman simulations the model is able to constrain the deviation away from a typical SN Ia template as a result of microlensing. Note that these simulations, along with BayeSN-TD, assume achromatic microlensing.
• Figure 3: As Fig. \ref{['roman_sim_plots']} but for LSST simulations of glSNe Ia presented by Arendse24 which incorporate a chromatic effect of microlensing.
• Figure 4: Left panels: Simulated 2-image LSST glSN Ia light curve from Arendse24 along with associated BayeSN-TD fits. Right panels: Plotted data points represent simulated deviation from model light curves as a result of microlensing, with associated uncertainties from measurement noise as true simulated values post-microlensing, without noise, are not available. These simulations include chromatic microlensing, therefore different filters are differently impacted. Plotted line and shaded region represent the posterior mean and standard deviation on microlensing from the achromatic treatment included in BayeSN-TD.
• Figure 5: As Fig. \ref{['LSST_example']} but for a particularly extreme example of microlensing. In this case, BayeSN-TD is able to identify that the peak of this light curve is driven by microlensing rather than the luminosity of the SN, and recover the true time delay within 1 day.